Truncated Fourier series of e in v over one period centred on zero: fourierSeries(e, v, period, n).
Like _Taylor, v is the expansion variable rather than a binder: it appears free in the result. It is kept out of children and carried through rebuild so substitute cannot rewrite the variable the expansion is taken in.
Unlike _Taylor, the coefficients are numeric: each is a definite integral evaluated by Simpson's rule, so period must reduce to a concrete positive number and the integrand must be evaluable over [-period/2, period/2]. Anything else leaves the node symbolic, the fixpoint convention shared with the transforms.
Not to be confused with transform._Fourier (fourier(e, t, w)), which is the Fourier transform -- a different operation with a different result type.